In-class Exercise 7: Calibrating Hedonic Pricing Model for Private Highrise Property with GWR Method

Author

Nguyen Bao Thu Phuong

Published

October 14, 2024

Modified

October 14, 2024

1 Getting started

1.1 Import R packages

First we import the relevant packages using p_load() of pacman.

pacman::p_load(olsrr, corrplot, ggpubr, sf, spdep, GWmodel, tmap, tidyverse, gtsummary, ggstatsplot, sfdep)

1.2 Import the Data

condo_resale = read_csv("data/aspatial/Condo_resale_2015.csv")
Rows: 1436 Columns: 23
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
dbl (23): LATITUDE, LONGITUDE, POSTCODE, SELLING_PRICE, AREA_SQM, AGE, PROX_...

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
mpsz = st_read(dsn = "data/geospatial", layer = "MP14_SUBZONE_WEB_PL") |>
  st_transform(3414)
Reading layer `MP14_SUBZONE_WEB_PL' from data source 
  `C:\thuphuong1110\ISSS626-GAA\In-class_Ex\In-class_Ex07\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21

2 Aspatial data wrangling

2.1 Convert aspatial data frame into an sf object

condo_resale.sf <- st_as_sf(condo_resale,
                            coords = c("LONGITUDE", "LATITUDE"),
                            crs=4326) %>%
  st_transform(crs=3414)

3 Correlation Analysis

ggcorrmat(condo_resale[,5:23])

4 Linear Regression

The code chunk below uses lm() to calibrate a multiple linear regression model.

condo.mlr <- lm(formula = SELLING_PRICE ~ AREA_SQM + AGE    + 
                  PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE +
                  PROX_URA_GROWTH_AREA + PROX_HAWKER_MARKET + PROX_KINDERGARTEN + 
                  PROX_MRT  + PROX_PARK + PROX_PRIMARY_SCH + 
                  PROX_TOP_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_SUPERMARKET + 
                  PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD + LEASEHOLD_99YR, 
                data=condo_resale.sf)
summary(condo.mlr)

Call:
lm(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE + 
    PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_HAWKER_MARKET + 
    PROX_KINDERGARTEN + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + 
    PROX_TOP_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_SUPERMARKET + 
    PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD + 
    LEASEHOLD_99YR, data = condo_resale.sf)

Residuals:
     Min       1Q   Median       3Q      Max 
-3471036  -286903   -22426   239412 12254549 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)           543071.4   136210.9   3.987 7.03e-05 ***
AREA_SQM               12688.7      370.1  34.283  < 2e-16 ***
AGE                   -24566.0     2766.0  -8.881  < 2e-16 ***
PROX_CBD              -78122.0     6791.4 -11.503  < 2e-16 ***
PROX_CHILDCARE       -333219.0   111020.3  -3.001 0.002734 ** 
PROX_ELDERLYCARE      170950.0    42110.8   4.060 5.19e-05 ***
PROX_URA_GROWTH_AREA   38507.6    12523.7   3.075 0.002147 ** 
PROX_HAWKER_MARKET     23801.2    29299.9   0.812 0.416739    
PROX_KINDERGARTEN     144098.0    82738.7   1.742 0.081795 .  
PROX_MRT             -322775.9    58528.1  -5.515 4.14e-08 ***
PROX_PARK             564487.9    66563.0   8.481  < 2e-16 ***
PROX_PRIMARY_SCH      186170.5    65515.2   2.842 0.004553 ** 
PROX_TOP_PRIMARY_SCH    -477.1    20598.0  -0.023 0.981525    
PROX_SHOPPING_MALL   -207721.5    42855.5  -4.847 1.39e-06 ***
PROX_SUPERMARKET      -48074.7    77145.3  -0.623 0.533273    
PROX_BUS_STOP         675755.0   138552.0   4.877 1.20e-06 ***
NO_Of_UNITS             -216.2       90.3  -2.394 0.016797 *  
FAMILY_FRIENDLY       142128.3    47055.1   3.020 0.002569 ** 
FREEHOLD              300646.5    77296.5   3.890 0.000105 ***
LEASEHOLD_99YR        -77137.4    77570.9  -0.994 0.320192    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 755800 on 1416 degrees of freedom
Multiple R-squared:  0.652, Adjusted R-squared:  0.6474 
F-statistic: 139.6 on 19 and 1416 DF,  p-value: < 2.2e-16

5 Model Assessment: olsrr method

ols_regress(condo.mlr)
                                Model Summary                                 
-----------------------------------------------------------------------------
R                            0.807       RMSE                     750537.537 
R-Squared                    0.652       MSE                571262902261.223 
Adj. R-Squared               0.647       Coef. Var                    43.160 
Pred R-Squared               0.637       AIC                       42971.173 
MAE                     412117.987       SBC                       43081.835 
-----------------------------------------------------------------------------
 RMSE: Root Mean Square Error 
 MSE: Mean Square Error 
 MAE: Mean Absolute Error 
 AIC: Akaike Information Criteria 
 SBC: Schwarz Bayesian Criteria 

                                     ANOVA                                       
--------------------------------------------------------------------------------
                    Sum of                                                      
                   Squares          DF         Mean Square       F         Sig. 
--------------------------------------------------------------------------------
Regression    1.515738e+15          19        7.977571e+13    139.648    0.0000 
Residual      8.089083e+14        1416    571262902261.223                      
Total         2.324647e+15        1435                                          
--------------------------------------------------------------------------------

                                               Parameter Estimates                                                
-----------------------------------------------------------------------------------------------------------------
               model           Beta    Std. Error    Std. Beta       t        Sig           lower          upper 
-----------------------------------------------------------------------------------------------------------------
         (Intercept)     543071.420    136210.918                   3.987    0.000     275874.535     810268.305 
            AREA_SQM      12688.669       370.119        0.579     34.283    0.000      11962.627      13414.710 
                 AGE     -24566.001      2766.041       -0.166     -8.881    0.000     -29991.980     -19140.022 
            PROX_CBD     -78121.985      6791.377       -0.267    -11.503    0.000     -91444.227     -64799.744 
      PROX_CHILDCARE    -333219.036    111020.303       -0.087     -3.001    0.003    -551000.984    -115437.089 
    PROX_ELDERLYCARE     170949.961     42110.748        0.083      4.060    0.000      88343.803     253556.120 
PROX_URA_GROWTH_AREA      38507.622     12523.661        0.059      3.075    0.002      13940.700      63074.545 
  PROX_HAWKER_MARKET      23801.197     29299.923        0.019      0.812    0.417     -33674.725      81277.120 
   PROX_KINDERGARTEN     144097.972     82738.669        0.030      1.742    0.082     -18205.570     306401.514 
            PROX_MRT    -322775.874     58528.079       -0.123     -5.515    0.000    -437586.937    -207964.811 
           PROX_PARK     564487.876     66563.011        0.148      8.481    0.000     433915.162     695060.590 
    PROX_PRIMARY_SCH     186170.524     65515.193        0.072      2.842    0.005      57653.253     314687.795 
PROX_TOP_PRIMARY_SCH       -477.073     20597.972       -0.001     -0.023    0.982     -40882.894      39928.747 
  PROX_SHOPPING_MALL    -207721.520     42855.500       -0.109     -4.847    0.000    -291788.613    -123654.427 
    PROX_SUPERMARKET     -48074.679     77145.257       -0.012     -0.623    0.533    -199405.956     103256.599 
       PROX_BUS_STOP     675755.044    138551.991        0.133      4.877    0.000     403965.817     947544.272 
         NO_Of_UNITS       -216.180        90.302       -0.046     -2.394    0.017       -393.320        -39.040 
     FAMILY_FRIENDLY     142128.272     47055.082        0.056      3.020    0.003      49823.107     234433.438 
            FREEHOLD     300646.543     77296.529        0.117      3.890    0.000     149018.525     452274.561 
      LEASEHOLD_99YR     -77137.375     77570.869       -0.030     -0.994    0.320    -229303.551      75028.801 
-----------------------------------------------------------------------------------------------------------------

The output shows that the condo.mlr model can explain close to 65% of the variation in the price.

5.1 Multicollinearity

ols_vif_tol(condo.mlr)
              Variables Tolerance      VIF
1              AREA_SQM 0.8601326 1.162611
2                   AGE 0.7011585 1.426211
3              PROX_CBD 0.4575471 2.185567
4        PROX_CHILDCARE 0.2898233 3.450378
5      PROX_ELDERLYCARE 0.5922238 1.688551
6  PROX_URA_GROWTH_AREA 0.6614081 1.511926
7    PROX_HAWKER_MARKET 0.4373874 2.286303
8     PROX_KINDERGARTEN 0.8356793 1.196631
9              PROX_MRT 0.4949877 2.020252
10            PROX_PARK 0.8015728 1.247547
11     PROX_PRIMARY_SCH 0.3823248 2.615577
12 PROX_TOP_PRIMARY_SCH 0.4878620 2.049760
13   PROX_SHOPPING_MALL 0.4903052 2.039546
14     PROX_SUPERMARKET 0.6142127 1.628100
15        PROX_BUS_STOP 0.3311024 3.020213
16          NO_Of_UNITS 0.6543336 1.528272
17      FAMILY_FRIENDLY 0.7191719 1.390488
18             FREEHOLD 0.2728521 3.664990
19       LEASEHOLD_99YR 0.2645988 3.779307

The result shows that no variable has VIF great than 5. Dummy variables will not affect the overall calibration a lot, that is why although FREEHOLD and LEASEHOLE_99YR have multicollinearity (as they are dummy variables derived from the same variable), their VIFs are still lower than 5.

5.2 Variable Selection

condo_fw_mlr = ols_step_forward_p(
  condo.mlr,
  p_val = 0.05,
  details = FALSE)
plot(condo_fw_mlr)

5.3 Test for Non-linearity

ols_plot_resid_fit(condo_fw_mlr$model)

The figure above reveals that most of the points scatter around the 0 line.

ols_plot_resid_hist(condo_fw_mlr$model)

ols_test_normality(condo_fw_mlr$model)
Warning in ks.test.default(y, "pnorm", mean(y), sd(y)): ties should not be
present for the one-sample Kolmogorov-Smirnov test
-----------------------------------------------
       Test             Statistic       pvalue  
-----------------------------------------------
Shapiro-Wilk              0.6856         0.0000 
Kolmogorov-Smirnov        0.1366         0.0000 
Cramer-von Mises         121.0768        0.0000 
Anderson-Darling         67.9551         0.0000 
-----------------------------------------------

As the p-value is smaller than 0.05, we reject the null hypothesis that the model resembles normal distribution.

5.4 Residual normality test

First we export the residuals of the hedonic pricing model and save it as a data frame.

mlr_output = as.data.frame(condo_fw_mlr$model$residuals) |>
  rename('FW_MLR_RES' = 'condo_fw_mlr$model$residuals')

Next we join the newly created data frame with condo_resale_sf object.

condo_resale_sf = cbind(condo_resale.sf,
                        mlr_output$FW_MLR_RES) |>
  rename('MLR_RES' = 'mlr_output.FW_MLR_RES')

Next we use tmap to display the distribution of the residuals on an interactive map.

tmap_mode("view")
tmap mode set to interactive viewing
tm_shape(mpsz) +
  tmap_options(check.and.fix = TRUE) + # to fix the issue in the mpsz layer
  tm_polygons(alpha = 0.4) +
  tm_shape(condo_resale_sf) +
  tm_dots(col = "MLR_RES",
          alpha = 0.6,
          style = "quantile")
Warning: The shape mpsz is invalid (after reprojection). See sf::st_is_valid
Variable(s) "MLR_RES" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
tmap_mode("plot")
tmap mode set to plotting

The map shows some high value clusters around the central region.

The Moran’s I test will be performed to prove our observations.

condo_resale_sf = condo_resale_sf |>
  mutate(nb = st_knn(geometry, k=6,
                     longlat = FALSE),
         wt = st_weights(nb,
                         style = "W"),
         .before = 1)
set.seed(1234)
global_moran_perm(condo_resale_sf$MLR_RES,
                  condo_resale_sf$nb,
                  condo_resale_sf$wt,
                  alternative = "two.sided",
                  nsim = 99)

    Monte-Carlo simulation of Moran I

data:  x 
weights: listw  
number of simulations + 1: 100 

statistic = 0.32254, observed rank = 100, p-value < 2.2e-16
alternative hypothesis: two.sided

As the p-value is smaller than 0.05, we can reject the null hypothesis that the residuals are randomly distributed. Since the Moran I’s statistic = 0.32254 > 0, we can infer that the residuals resemble cluster distribution.

6 Build Fixed Bandwidth GWR model

bw_fixed = bw.gwr(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
                  data = condo_resale_sf,
                  approach = 'CV',
                  kernel = 'gaussian',
                  adaptive = FALSE,
                  longlat = FALSE)
Fixed bandwidth: 17660.96 CV score: 8.259118e+14 
Fixed bandwidth: 10917.26 CV score: 7.970454e+14 
Fixed bandwidth: 6749.419 CV score: 7.273273e+14 
Fixed bandwidth: 4173.553 CV score: 6.300006e+14 
Fixed bandwidth: 2581.58 CV score: 5.404958e+14 
Fixed bandwidth: 1597.687 CV score: 4.857515e+14 
Fixed bandwidth: 989.6077 CV score: 4.722431e+14 
Fixed bandwidth: 613.7939 CV score: 1.378294e+16 
Fixed bandwidth: 1221.873 CV score: 4.778717e+14 
Fixed bandwidth: 846.0596 CV score: 4.791629e+14 
Fixed bandwidth: 1078.325 CV score: 4.751406e+14 
Fixed bandwidth: 934.7772 CV score: 4.72518e+14 
Fixed bandwidth: 1023.495 CV score: 4.730305e+14 
Fixed bandwidth: 968.6643 CV score: 4.721317e+14 
Fixed bandwidth: 955.7206 CV score: 4.722072e+14 
Fixed bandwidth: 976.6639 CV score: 4.721387e+14 
Fixed bandwidth: 963.7202 CV score: 4.721484e+14 
Fixed bandwidth: 971.7199 CV score: 4.721293e+14 
Fixed bandwidth: 973.6083 CV score: 4.721309e+14 
Fixed bandwidth: 970.5527 CV score: 4.721295e+14 
Fixed bandwidth: 972.4412 CV score: 4.721296e+14 
Fixed bandwidth: 971.2741 CV score: 4.721292e+14 
Fixed bandwidth: 970.9985 CV score: 4.721293e+14 
Fixed bandwidth: 971.4443 CV score: 4.721292e+14 
Fixed bandwidth: 971.5496 CV score: 4.721293e+14 
Fixed bandwidth: 971.3793 CV score: 4.721292e+14 
Fixed bandwidth: 971.3391 CV score: 4.721292e+14 
Fixed bandwidth: 971.3143 CV score: 4.721292e+14 
Fixed bandwidth: 971.3545 CV score: 4.721292e+14 
Fixed bandwidth: 971.3296 CV score: 4.721292e+14 
Fixed bandwidth: 971.345 CV score: 4.721292e+14 
Fixed bandwidth: 971.3355 CV score: 4.721292e+14 
Fixed bandwidth: 971.3413 CV score: 4.721292e+14 
Fixed bandwidth: 971.3377 CV score: 4.721292e+14 
Fixed bandwidth: 971.34 CV score: 4.721292e+14 
Fixed bandwidth: 971.3405 CV score: 4.721292e+14 
Fixed bandwidth: 971.3408 CV score: 4.721292e+14 
Fixed bandwidth: 971.3403 CV score: 4.721292e+14 
Fixed bandwidth: 971.3406 CV score: 4.721292e+14 
Fixed bandwidth: 971.3404 CV score: 4.721292e+14 
Fixed bandwidth: 971.3405 CV score: 4.721292e+14 
Fixed bandwidth: 971.3405 CV score: 4.721292e+14 

The result shows that the recommended bandwith is 971.3405 metres.

6.1 GWModel method - fixed bandwidth

gwr_fixed = gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
                  data = condo_resale_sf,
                  bw = bw_fixed,
                  kernel = 'gaussian',
                  longlat = FALSE)
gwr_fixed
   ***********************************************************************
   *                       Package   GWmodel                             *
   ***********************************************************************
   Program starts at: 2024-10-14 22:21:59.318987 
   Call:
   gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + 
    PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + 
    PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + 
    PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD, 
    data = condo_resale_sf, bw = bw_fixed, kernel = "gaussian", 
    longlat = FALSE)

   Dependent (y) variable:  SELLING_PRICE
   Independent variables:  AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE PROX_URA_GROWTH_AREA PROX_MRT PROX_PARK PROX_PRIMARY_SCH PROX_SHOPPING_MALL PROX_BUS_STOP NO_Of_UNITS FAMILY_FRIENDLY FREEHOLD
   Number of data points: 1436
   ***********************************************************************
   *                    Results of Global Regression                     *
   ***********************************************************************

   Call:
    lm(formula = formula, data = data)

   Residuals:
     Min       1Q   Median       3Q      Max 
-3470778  -298119   -23481   248917 12234210 

   Coefficients:
                          Estimate Std. Error t value Pr(>|t|)    
   (Intercept)           527633.22  108183.22   4.877 1.20e-06 ***
   AREA_SQM               12777.52     367.48  34.771  < 2e-16 ***
   AGE                   -24687.74    2754.84  -8.962  < 2e-16 ***
   PROX_CBD              -77131.32    5763.12 -13.384  < 2e-16 ***
   PROX_CHILDCARE       -318472.75  107959.51  -2.950 0.003231 ** 
   PROX_ELDERLYCARE      185575.62   39901.86   4.651 3.61e-06 ***
   PROX_URA_GROWTH_AREA   39163.25   11754.83   3.332 0.000885 ***
   PROX_MRT             -294745.11   56916.37  -5.179 2.56e-07 ***
   PROX_PARK             570504.81   65507.03   8.709  < 2e-16 ***
   PROX_PRIMARY_SCH      159856.14   60234.60   2.654 0.008046 ** 
   PROX_SHOPPING_MALL   -220947.25   36561.83  -6.043 1.93e-09 ***
   PROX_BUS_STOP         682482.22  134513.24   5.074 4.42e-07 ***
   NO_Of_UNITS             -245.48      87.95  -2.791 0.005321 ** 
   FAMILY_FRIENDLY       146307.58   46893.02   3.120 0.001845 ** 
   FREEHOLD              350599.81   48506.48   7.228 7.98e-13 ***

   ---Significance stars
   Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
   Residual standard error: 756000 on 1421 degrees of freedom
   Multiple R-squared: 0.6507
   Adjusted R-squared: 0.6472 
   F-statistic: 189.1 on 14 and 1421 DF,  p-value: < 2.2e-16 
   ***Extra Diagnostic information
   Residual sum of squares: 8.120609e+14
   Sigma(hat): 752522.9
   AIC:  42966.76
   AICc:  42967.14
   BIC:  41731.39
   ***********************************************************************
   *          Results of Geographically Weighted Regression              *
   ***********************************************************************

   *********************Model calibration information*********************
   Kernel function: gaussian 
   Fixed bandwidth: 971.3405 
   Regression points: the same locations as observations are used.
   Distance metric: Euclidean distance metric is used.

   ****************Summary of GWR coefficient estimates:******************
                               Min.     1st Qu.      Median     3rd Qu.
   Intercept            -3.5988e+07 -5.1998e+05  7.6780e+05  1.7412e+06
   AREA_SQM              1.0003e+03  5.2758e+03  7.4740e+03  1.2301e+04
   AGE                  -1.3475e+05 -2.0813e+04 -8.6260e+03 -3.7784e+03
   PROX_CBD             -7.7047e+07 -2.3608e+05 -8.3600e+04  3.4646e+04
   PROX_CHILDCARE       -6.0097e+06 -3.3667e+05 -9.7425e+04  2.9007e+05
   PROX_ELDERLYCARE     -3.5000e+06 -1.5970e+05  3.1971e+04  1.9577e+05
   PROX_URA_GROWTH_AREA -3.0170e+06 -8.2013e+04  7.0749e+04  2.2612e+05
   PROX_MRT             -3.5282e+06 -6.5836e+05 -1.8833e+05  3.6922e+04
   PROX_PARK            -1.2062e+06 -2.1732e+05  3.5383e+04  4.1335e+05
   PROX_PRIMARY_SCH     -2.2695e+07 -1.7066e+05  4.8472e+04  5.1555e+05
   PROX_SHOPPING_MALL   -7.2585e+06 -1.6684e+05 -1.0517e+04  1.5923e+05
   PROX_BUS_STOP        -1.4676e+06 -4.5207e+04  3.7601e+05  1.1664e+06
   NO_Of_UNITS          -1.3170e+03 -2.4822e+02 -3.0846e+01  2.5496e+02
   FAMILY_FRIENDLY      -2.2749e+06 -1.1140e+05  7.6214e+03  1.6107e+05
   FREEHOLD             -9.2067e+06  3.8073e+04  1.5169e+05  3.7528e+05
                             Max.
   Intercept            112793548
   AREA_SQM                 21575
   AGE                     434201
   PROX_CBD               2704596
   PROX_CHILDCARE         1654087
   PROX_ELDERLYCARE      38867814
   PROX_URA_GROWTH_AREA  78515730
   PROX_MRT               3124316
   PROX_PARK             18122425
   PROX_PRIMARY_SCH       4637503
   PROX_SHOPPING_MALL     1529952
   PROX_BUS_STOP         11342182
   NO_Of_UNITS              12907
   FAMILY_FRIENDLY        1720744
   FREEHOLD               6073636
   ************************Diagnostic information*************************
   Number of data points: 1436 
   Effective number of parameters (2trace(S) - trace(S'S)): 438.3804 
   Effective degrees of freedom (n-2trace(S) + trace(S'S)): 997.6196 
   AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 42263.61 
   AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 41632.36 
   BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 42515.71 
   Residual sum of squares: 2.53407e+14 
   R-square value:  0.8909912 
   Adjusted R-square value:  0.8430417 

   ***********************************************************************
   Program stops at: 2024-10-14 22:22:00.406847 

The output shows that the adjust R-square improve quite a lot to 84.3% compared to the global model (64.7%).

7 Build adaptive bandwith GWR model

bw_adaptive = bw.gwr(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
                  data = condo_resale_sf,
                  approach = 'CV',
                  kernel = 'gaussian',
                  adaptive = TRUE,
                  longlat = FALSE)
Adaptive bandwidth: 895 CV score: 7.952401e+14 
Adaptive bandwidth: 561 CV score: 7.667364e+14 
Adaptive bandwidth: 354 CV score: 6.953454e+14 
Adaptive bandwidth: 226 CV score: 6.15223e+14 
Adaptive bandwidth: 147 CV score: 5.674373e+14 
Adaptive bandwidth: 98 CV score: 5.426745e+14 
Adaptive bandwidth: 68 CV score: 5.168117e+14 
Adaptive bandwidth: 49 CV score: 4.859631e+14 
Adaptive bandwidth: 37 CV score: 4.646518e+14 
Adaptive bandwidth: 30 CV score: 4.422088e+14 
Adaptive bandwidth: 25 CV score: 4.430816e+14 
Adaptive bandwidth: 32 CV score: 4.505602e+14 
Adaptive bandwidth: 27 CV score: 4.462172e+14 
Adaptive bandwidth: 30 CV score: 4.422088e+14 
gwr_adaptive = gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
                  data = condo_resale_sf,
                  bw = bw_adaptive,
                  adaptive = TRUE,
                  kernel = 'gaussian',
                  longlat = FALSE)

7.1 Convert SDF into sf data.frame

gwr_adaptive_output = as.data.frame(
  gwr_adaptive$SDF) |>
  select(-c(2:15))
gwr_sf_adaptive = cbind(condo_resale_sf,
                        gwr_adaptive_output)

7.2 Visualize Local R2

tmap_mode("view")
tmap mode set to interactive viewing
tm_shape(mpsz)+
  tmap_options(check.and.fix = TRUE) +
  tm_polygons(alpha = 0.1) +
tm_shape(gwr_sf_adaptive) +  
  tm_dots(col = "Local_R2",
          border.col = "gray60",
          border.lwd = 1) +
  tm_view(set.zoom.limits = c(11,14))
Warning: The shape mpsz is invalid (after reprojection). See sf::st_is_valid
tmap_mode('plot')
tmap mode set to plotting